Why can't the growth rate be higher than the discount rate?
Why can't the discount rate be lower than the growth rate in terminal value?
What is the theoretical reason for it.
Ways to Calculate Terminal Value
Terminal value is an important part in determining company valuation. Before digging in to the theoretical explanation to the above question, here's a quick review of the calculation. Depending on various factors, you may want to use an exit multiple or perpetual growth method, such as the Gordon Growth Model for determining terminal value in a DCF model.
- Perpetual Growth: Use when company is in its long-term, mature growth phase
- Terminal Value = Last Year Free Cash Flow x ((1 + Terminal Growth Rate) / (WACC - Terminal Growth Rate))
- Exit Multiple: Use when company is not yet in steady growth phase or when market has a good idea of acquisition value (ex: LBO)
For more information on how to find your growth rate and discount rate, check out these posts:
Remember, no matter what formula and inputs you use, it is just an approximation or attempt to model a complex real world process.
How Growth Rate and Discount Rate Impact Terminal Value Formula
From a simple mathematical perspective, the growth rate can't be higher than the discount rate because it would give you a negative terminal value. From a theoretical perspective, Certified Investment Banking Professional – 1st Year Associate @jhoratio" explains:
Growth rates can exceed the cost of capital for very short periods of time, but we're talking about a growth rate IN PERPETUITY here. Any company whose growth rate exceeds the required rate of return would a) be a riskless arbitrage and b) attract all the money in the world to invest in it. The company would eventually become the entire economy with every human being on earth working for it.